A number of reservoir simulators and wellbore simulators exist as stand-alone products. The most common way of coupling a wellbore simulator and reservoir simulator is by means of well productivity index. The wellbore simulators are based on a finite difference scheme and solve the Navier Stokes equation. Using the pressures obtained from the wellbore simulation, a productivity index (PI) or Well Index (WI) can be determined. This PI is used as an input to the reservoir simulator. Some of the assumptions that are made in the coupling include flow being vertical and upward, or using a predetermined table of temperature and pressures. Another approach involves treating the wellbore as a point source in a reservoir and using a Peaceman solution to determine the pressure distribution inside a grid block.
Temperature coupling between wellbore and reservoir is used to model geothermal systems where the field of interest is the fluid temperature. There is no mixing of fluids between the reservoir and wellbore.
Generally, there has been no attempt to drive a fracture in the reservoir by means of the pressures being tied between the wellbore and the rock formation.